Entropy最新文献

Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, we are referring to the classical entropies: the Boltzmann-Gibbs, von Neumann, Shannon, Kolmogorov-Sinai and topological entropies. In addition to their common name, which is historically justified (as we briefly describe in this review), another commonality of the classical entropies is the important role that they have played and are still playing in the theory and applications of their respective fields and beyond. Therefore, it is not surprising that, in the course of time, many other instances of the overarching concept of entropy have been proposed, most of them tailored to specific purposes. Following the current usage, we will refer to all of them, whether classical or new, simply as entropies. In particular, the subject of this review is their applications in data analysis and machine learning. The reason for these particular applications is that entropies are very well suited to characterize probability mass distributions, typically generated by finite-state processes or symbolized signals. Therefore, we will focus on entropies defined as positive functionals on probability mass distributions and provide an axiomatic characterization that goes back to Shannon and Khinchin. Given the plethora of entropies in the literature, we have selected a representative group, including the classical ones. The applications summarized in this review nicely illustrate the power and versatility of entropy in data analysis and machine learning.

Allostatic self-efficacy (ASE) represents a computational theory of fatigue and depression. In brief, it postulates that (i) fatigue is a feeling state triggered by a metacognitive diagnosis of loss of control over bodily states (persistently elevated interoceptive surprise); and that (ii) generalization of low self-efficacy beliefs beyond bodily control induces depression. Here, we converted ASE theory into a structural causal model (SCM). This allowed identification of empirically testable hypotheses regarding causal relationships between the variables of interest. Applying conditional independence tests to questionnaire data from healthy volunteers, we sought to identify contradictions to the proposed SCM. Moreover, we estimated two causal effects proposed by ASE theory using three different methods. Our analyses identified specific aspects of the proposed SCM that were inconsistent with the available data. This enabled formulation of an updated SCM that can be tested against future data. Second, we confirmed the predicted negative average causal effect from metacognition of allostatic control to fatigue across all three different methods of estimation. Our study represents an initial attempt to refine and formalize ASE theory using methods from causal inference. Our results confirm key predictions from ASE theory but also suggest revisions which require empirical verification in future studies.

In this paper, we introduce the workflow for converting qubit circuits represented by Open Quantum Assembly format (OpenQASM, also known as QASM) into the qudit form for execution on qudit hardware and provide a method for translating qudit experiment results back into qubit results. We present the comparison of several qudit transpilation regimes, which differ in decomposition of multicontrolled gates: qubit as ordinary qubit transpilation and execution, qutrit with d=3 levels and single qubit in qudit, and ququart with d=4 levels and 2 qubits per ququart. We provide several examples of transpiling circuits for trapped ion qudit processors, which demonstrate potential advantages of qudits.

We investigated the optimal performance of an irreversible Stirling-like heat engine described by both overdamped and underdamped models within the framework of stochastic thermodynamics. By establishing a link between energy dissipation and Wasserstein distance, we derived the upper bound of maximal power that can be delivered over a complete engine cycle for both models. Additionally, we analytically developed an optimal control strategy to achieve this upper bound of maximal power and determined the efficiency at maximal power in the overdamped scenario.

Image segmentation is a crucial task in artificial intelligence fields such as computer vision and medical imaging. While convolutional neural networks (CNNs) have achieved notable success by learning representative features from large datasets, they often lack geometric priors and global object information, limiting their accuracy in complex scenarios. Variational methods like active contours provide geometric priors and theoretical interpretability but require manual initialization and are sensitive to hyper-parameters. To overcome these challenges, we propose a novel segmentation approach, named PolarVoting, which combines the minimal path encoding rich geometric features and CNNs which can provide efficient initialization. The introduced model involves two main steps: firstly, we leverage the PolarMask model to extract multiple source points for initialization, and secondly, we construct a voting score map which implicitly contains the segmentation mask via a modified circular geometric voting (CGV) scheme. This map embeds global geometric information for finding accurate segmentation. By integrating neural network representation with geometric priors, the PolarVoting model enhances segmentation accuracy and robustness. Extensive experiments on various datasets demonstrate that the proposed PolarVoting method outperforms both PolarMask and traditional single-source CGV models. It excels in challenging imaging scenarios characterized by intensity inhomogeneity, noise, and complex backgrounds, accurately delineating object boundaries and advancing the state of image segmentation.

Learning is a fundamental property of intelligent systems, observed across biological organisms and engineered systems. While modern intelligent systems typically rely on gradient descent for learning, the need for exact gradients and complex information flow makes its implementation in biological and neuromorphic systems challenging. This has motivated the exploration of alternative learning mechanisms that can operate locally and do not rely on exact gradients. In this work, we introduce a novel approach that leverages noise in the parameters of the system and global reinforcement signals. Using an Ornstein-Uhlenbeck process with adaptive dynamics, our method balances exploration and exploitation during learning, driven by deviations from error predictions, akin to reward prediction error. Operating in continuous time, Ornstein-Uhlenbeck adaptation (OUA) is proposed as a general mechanism for learning in dynamic, time-evolving environments. We validate our approach across a range of different tasks, including supervised learning and reinforcement learning in feedforward and recurrent systems. Additionally, we demonstrate that it can perform meta-learning, adjusting hyper-parameters autonomously. Our results indicate that OUA provides a promising alternative to traditional gradient-based methods, with potential applications in neuromorphic computing. It also hints at a possible mechanism for noise-driven learning in the brain, where stochastic neurotransmitter release may guide synaptic adjustments.

The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict and exhaustive formulation. In the previous article, it was shown that two of the three most famous thermodynamic formulations of the Second Law of Thermodynamics are non-exhaustive. However, the status of the statistical approach, contrary to common and unfounded opinions, is even more difficult. It is known that Boltzmann did not manage to completely and correctly derive the Second Law of Thermodynamics from statistical mechanics, even though he probably did everything he could in this regard. In particular, he introduced molecular chaos into the extension of the Liouville equation, obtaining the Boltzmann equation. By using the H theorem, Boltzmann transferred the Second Law of Thermodynamics thesis to the molecular chaos hypothesis, which is not considered to be fully true. Therefore, the authors present a detailed and critical review of the issue of the Second Law of Thermodynamics and entropy from the perspective of phenomenological thermodynamics and statistical mechanics, as well as kinetic theory. On this basis, Propositions 1-3 for the statements of the Second Law of Thermodynamics are formulated in the original part of the article. Proposition 1 is based on resolving the misunderstanding of the Perpetuum Mobile of the Second Kind by introducing the Perpetuum Mobile of the Third Kind. Proposition 2 specifies the structure of allowed thermodynamic processes by using the Inequality of Heat and Temperature Proportions inspired by Eudoxus of Cnidus's inequalities defining real numbers. Proposition 3 is a Probabilistic Scheme of the Second Law of Thermodynamics that, like a game, shows the statistical tendency for entropy to increase, even though the possibility of it decreasing cannot be completely ruled out. Proposition 3 is, in some sense, free from Loschmidt's irreversibility paradox.

This paper analyzes the behavior of the entropy of a nuclear fuel rod under deep burnup conditions, beyond standard operational ranges, reaching up to 60 years. The evolution of the neutron source distribution in a pressurized water reactor (PWR) fuel pin was analyzed using the Monte Carlo method and Shannon information entropy. To maintain proper statistics, a novel scaling method was developed, adjusting the neutron population based on the fission rate. By integrating reactor physics with information theory, this work aimed at the deeper understanding of nuclear fuel behavior under extreme burnup conditions. The results show a "U-shaped" entropy evolution: an initial decrease due to self-organization, followed by stabilization and eventual increase due to degradation. A minimum entropy state is reached after approximately 45 years of pin operation, showing a steady-state condition with no entropy change. This point may indicate a physical limit for fuel utilization. Beyond this point, entropy rises, reflecting system degradation and lower energy efficiency. The results show that entropy analysis can provide valuable insights into fuel behavior and operational limits. The proposed scaling method may also serve to control a Monte Carlo simulation, especially for the analysis of long-life reactors.

This paper deals with the topics of modeling joint distributions on a generalized probability space. An algebraic structure known as quantum logic is taken as the basic model. There is a brief summary of some earlier published findings concerning a function s-map, which is a mathematical tool suitable for constructing virtual joint probabilities of even non-compatible propositions. The paper completes conclusions published in 2020 and extends the results for three or more random variables if the marginal distributions are known. The existence of a (n+1)-variate joint distribution is shown in special cases when the quantum logic consists of at most n blocks of Boolean algebras.

Entropies for alkane isomers longer than C₁₀ are computed using our recently developed linear regression model for thermochemical properties which is based on second-order group contributions. The computed entropies show excellent agreement with experimental data and data from Scott's tables which are obtained from a statistical mechanics-based correlation. Entropy production and heat input are calculated for the hydroisomerization of C₇ isomers in various zeolites (FAU-, ITQ-29-, BEA-, MEL-, MFI-, MTW-, and MRE-types) at 500 K at chemical equilibrium. Small variations in these properties are observed because of the differences in reaction equilibrium distributions for these zeolites. The effect of chain length on heat input and entropy production is also studied for the hydroisomerization of C₇, C₈, C₁₀, and C₁₄ isomers in MTW-type zeolite at 500 K. For longer chains, both heat input and entropy production increase. Enthalpies and absolute entropies of C₇ hydroisomerization reaction products in MTW-type zeolite increase with higher temperatures. These findings highlight the accuracy of our linear regression model in computing entropies for alkanes and provide insight for designing and optimizing zeolite-catalyzed hydroisomerization processes.